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Spectrally Efficient Bidirectional Decode-And Spectrally Efficient Bidirectional Decode-and-Forward Relaying for Wireless Networks von Diplom-Ingenieur Tobias Josef Oechtering aus Rheine von der Fakultät IV - Elektrotechnik und Informatik der Technischen Universität Berlin zur Erlangung des akademischen Grades Doktor der Ingenieurwissenschaften – Dr.-Ing. – genehmigte Dissertation Promotionsausschuss Vorsitzender: Prof. Dr.-Ing. habil. Gerhard Mönich 1. Berichter: Prof. Dr.-Ing. Dr. rer. nat. Holger Boche, 2. Berichter: Prof. Dr.-Ing. Dr.-Ing. E. h. Joachim Hagenauer Tag der wissenschaftlichen Aussprache: 09.10.2007 Berlin, 2007 D83 ii Zusammenfassung Relaiskonzepte werden in Zunkuft in drahtlosen Netzwerken eine zentrale Rolle spielen. In dieser Dissertation wird ein Netzwerk mit drei Stationen betrachtet, in welchem zwei Stationen mittels einer Relaisstation miteinander kommunizieren. Wir untersuchen ein Zweiphasenprotokoll ohne Rückkopplung, in dem die Relaisstation die Nachrichten für beide Richtungen gleichzeitig dekodiert und weiterleitet. Damit kann der spektrale Ver- lust, verursacht durch halbduplexe Stationen in unidirektionalen Protokollen, kompensiert werden. Im ersten Abschnitt geht es um schichtübergreifende Konzepte für die bidirektionale Re- laiskommunikation basierend auf dem Prinzip der Superpositionskodierung. Die Betrach- tungen werden für die festgelegte und optimale Zeitaufteilung der Phasen durchgeführt. Eine ausführliche Untersuchung der Kombinatorik der erreichbaren Ratenregion für Stationen mit einer Antenne erlaubt es uns die Ratenpaare, bei denen die Summe der gewichteten Raten maximiert wird, explizit zu bestimmen. Diese Untersuchungen werden am Beispiel der pa- ritätischen und der optimalen Zeitaufteilung ausgeführt. Die optimalen Ratenpaare werden im Weiteren für den Entwurf einer durchsatzoptimalen Ressourcenallokationsstrategie und für ein Relaisauswahlkriterium in einem Netzwerk mit N Relaisstationen verwendet. Dabei ist es vorteilhaft, die abwechselnde Nutzung ver- schiedener Relaisstationen zu erlauben. Außerdem stellen wir fest, dass die Summe eines jeden Ratenpaares auf dem Rand der ergodischen Ratenregion für unabhängige und identisch rayleighverteilte Schwundkanäle asymptotisch mit log(log(N)) wächst. Als nächstes betrachten wir den Fall, dass die Relaisstation eine Nachricht zusätzlich zur bidirektionalen Relaiskommunikation an beide Stationen übeträgt. Es zeigt sich, dass es immer optimal ist die Relaisnachricht zuerst zu dekodieren. Die gemeinsame Ressourcenal- lokation verbessert die Gesamteffizienz und ermöglicht einen neuen Ratenabtausch. Darüber hinaus charakterisieren und diskutieren wir das gemeinsame Summenratenmaximum beider Routingaufgaben. Anschließend untersuchen wir die erreichbaren Ratenregionen der bidirektionalen Re- laiskommunikation zwischen Stationen mit mehreren Antennen. Wir spezifizieren die op- timale Sendestrategie und zeigen, dass die Summe eines jeden Ratenpaares auf dem Rand der erreichbaren Ratenregion linear gemäß der räumlichen Dimension des Vektorkanals und der Zeitaufteilung der Phasen ansteigt. iv Zusammenfassung Im zweiten Abschnitt beweisen wir eine optimale Kanalkodierungsstrategie für den bidirek- tionalen Broadcastkanal mit einem endlichen Alphabet. Dabei werden erreichbare Raten bezüglich der maximalen Fehlerwahrscheinlichkeit betrachtet. Beim Kodierungssatz folgen wir der Philosophie der Netzwerkkodierung, die besagt, dass sich Informationsflüsse nicht wie Flüssigkeiten verhalten. Im abschließenden Resümee geben wir einen Ausblick auf zukünftige Forschungsarbeiten und präsentieren Beispiele wie bidirektionale Relaiskommunikation in drahtlose Netzwerke integriert werden kann. v Abstract Relaying concepts will play a central role in future wireless networks. In this thesis we consider a three-node network where two nodes communicate with each other by the support of a relay node. We study a two-phase decode-and-forward bidirectional relaying protocol without feedback. Bidirectional relaying has the ability to compensate the spectral loss due to the half-duplex constraint of nodes in wireless communications. In the first part we study cross-layer design aspects of bidirectional relaying using super- position encoding at the relay node. For the two phases we consider the fixed and optimal time division case. For single-antenna nodes an intensive study of the combinatorial struc- ture of the achievable rate region allows us to characterize the rate pairs which maximize the weighted rate sum for the equal and fixed time division case in closed form. These are used for the design of a throughput optimal resource allocation policy based on the backpressure strategy and to derive a relay selection criterion for routing in network with N relay nodes. It shows that it is beneficial to allow time-sharing between the usage of relay nodes. We see that the sum of any rate pair on the boundary of the ergodic rate region for independent and identical distributed Rayleigh fading channels grows asymptotically with log(log(N)). Then we add a relay multicast to the bidirectional relay communication. The joint resource allocation of two routing tasks improves the overall efficiency and enables new rate trade- offs. It shows that it is always optimal to decode the relay message first. Furthermore, we characterize and discuss the total sum-rate maximum of both routing tasks. After that we study the achievable rate region of bidirectional relaying between nodes equipped with multiple antennas. Therefore, we specify the optimal transmit strategy and show that the achievable rate region scales linearly with respect to the spatial degrees of the vector channels and time division. In the second part we find an optimal channel coding strategy for the bidirectional broadcast channel considering finite size alphabets. Thereby, we consider achievable rates with respect to the maximal probability of error. For the coding theorem we follow the philosophy of network coding and regard information flows not as “fluids”. In the final conclusion we give an outlook on future research work and show how the bidi- rectional relaying protocol can be integrated in wireless networks. vi Contents 1 Introduction 1 1.1 Trends and Motivations – Related Literature . 1 1.2 Contribution and Outline of the Thesis . 10 2 Bidirectional Relay Communication using Superposition Encoding 15 2.1 Introduction.................................. 15 2.2 Achievable Rate Region . 18 2.2.1 GaussianChannel........................... 18 2.2.2 Multiple Access Phase . 21 2.2.3 BroadcastPhase ........................... 23 2.2.4 Bidirectional Achievable Rate Region . 26 2.2.5 Achievable Rate Regions with Power Scaling . 42 2.3 Throughput Optimal Resource Allocation . 51 2.3.1 Stability Region . 53 2.3.2 Numerical Simulation . 58 2.4 RelaySelection ................................ 61 2.4.1 Relay Selection Criterion . 63 2.4.2 Scaling Law of the Ergodic Rate Region . 67 2.5 Piggyback a Common Relay Message . 75 2.5.1 Broadcast Phase with Relay Multicast . 78 2.5.2 Total Sum-Rate Maximum . 80 2.5.3 Combinatorial Discussion and Working Examples . 85 2.6 Extension to Multi-Antenna Bidirectional Relaying . 103 2.6.1 MIMO Multiple Access Phase . 107 2.6.2 MIMOBroadcastPhase . 112 2.6.3 MIMO Bidirectional Achievable Rate Region . 117 2.7 Discussion................................... 120 2.8 Appendix:Proofs ............................... 125 vii Contents 3 Optimal Coding Strategy for the Bidirectional Broadcast Channel 181 3.1 Introduction.................................. 181 3.1.1 Two-Phase Bidirectional Relay Channel . 182 3.1.2 Capacity Region of the Multiple Access Phase . 184 3.2 Capacity Region of the Broadcast Phase . 184 3.2.1 Proof of Achievability . 186 3.2.2 Proofofweakconverse. 192 3.2.3 Cardinality of set ......................... 194 U 3.3 Achievable Bidirectional Rate Region . 195 3.4 Example with Binary Channels . 196 3.5 Discussion and Further Results . 198 4 Conclusion and Future Work 201 References 207 viii List of Figures 2.1 Bidirectional relaying between single-antenna nodes . 15 2.2 Bidirectional achievable rate regions . 28 2.3 Contour plot of sum-rate maximum . 35 2.4 Equivalent characterization of .................... 39 RBRopt 2.5 Weighted rate sum optimal rate pairs . 41 2.6 Achievable rate region ˜ (with scaled powers) . 50 RBRopt 2.7 Queueingmodel................................ 52 2.8 Rate and stability regions of different policies . 59 2.9 Queue length evolutions of different policies . 60 2.10 Achievable rate region of relay selection with time-sharing . 66 2.11 Growth of the ergodic rate region with relay selection . 72 2.12 Upper and lower bounds on scaling law . 73 ⋆ 2.13 Cases where RBC(γR) intersects the boundary of the MAC capacity region 86 2.14 Rate trade-offs for constant total sum-rate . 90 2.15 Characteristic angles of α and (1 α) .............. 95 CMAC − RBC 2.16 Total sum-rate optimal rate pairs with respect to the time division . 98 2.17 Total sum-rate maximum with respect to the time division . 101 2.18 Piggyback achievable rate region for equal time division . 102 2.19 Piggyback achievable rate region for optimal time division . 102 2.20 Bidirectional relaying between multiple antenna nodes . 103 2.21 MIMO achievable rate region . 118 2.22 Combinatorial discussion for the proof of Theorem 2.5 . 127 2.23 Combinatorial discussion for the proof of Lemma 2.46 . 170 3.1 Two-phase decode-and-forward bidirectional relay channel without feedback 183 3.2 Achievable rate regions for binary symmetric channels . 198 4.1 Cellular coverage extension
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